The score on a trivia game is obtained by subtracting the number of incorrect answers from twice the number of correct answers. If a player answered 40 questions and obtained a score of 50, how many questions did the player answer correctly?
Correct answer: B. 30
- A. 20
- B. 30
- C. 35
- D. 40
Explanation
The correct answer is 30. Let x represent the number of correct answers from the player and y represent the number of incorrect answers from the player. Since the player answered 40 questions in total, the equation x + y = 40 represents this situation. Also, since the score is found by subtracting the number of incorrect answers from twice the number of correct answers and the player received a score of 50, the equation 2x - y = 50 represents this situation. Adding the system of two equations together yields (x + y) + (2x - y) = 40 + 50. This can be rewritten as 3x = 90. Finally, solving for x by dividing both sides of the equation by 3 yields x = 30.
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Quantitative reasoning applies arithmetic and basic algebra to numerical relationships, including percentages, ratios, averages, fractions, proportions, profit and loss, rates, time, work and measurement. Questions focus on translating words into equations, choosing an efficient method and checking whether the result is numerically reasonable.
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